Lots of great suggestions already. We live in London, I'll just add a couple of things:
1. "he loves history hence the NHM". NHM is about animals/dinosaurs (it's good, huge amount to see). If he loves history my number one recommendation would be the Tower of London, a bit pricey but worth it IMO. Imperial War Museum and Cabinet War Rooms are also good, depending on his specific areas of interest.
2. Changing of the guards might interest him?
3. There is a new "horrible histories" boat tour on the Thames this summer. Can't recommend personally as I haven't done it but reviews look good. If he likes Horrible Histories this might be one to consider, if not I would
highly recommend one of the boat tours with commentary as they are very entertaining, you see loads and learn a lot (City Cruises is the one we usually use - you can buy a hop on hop off day pass, there are loads of docks they stop at but they do stop in front of the Tower and also in front of London Eye/ Shrek's /Dungeons).
4. If time is pressed I would also leave off Madam Tussaud's. Don't understand the attraction (but understand you have it included in your pass). I've been there myself but never taken my kids even though we live not far from it. I walked past it this morning at about 9am and there was a queue waiting for it to open. Baffling.
5. Kensington is fine as an area to stay (and obviously handy for NHM and Science Museum - which is fantastic), but as recommended above, the area around County Hall might be a bit more convenient.
6. I still think Camden Market is fun for a 10 year old, but food is really a bit of a rip off there now. Was just there a few weeks ago with the kids, we live really close but hardly ever go! Borough Market is great for foodies.
7. Museum of London is free and pretty good. Postman's Park and St. Paul's Cathedral are both close by and the Millennium ("wobbly") bridge not far. To the east the Sky Garden and the Monument are also in this area ("The City").
8. Public transport is generally good and pretty easy, but the Circle and District lines have been not great over the last year (another reason to perhaps reconsider Kensington to stay). Your son doesn't need a ticket for the tube or bus as he is under 11, as long as he stays with you to travel. If he goes anywhere by himself he will need a ticket. Don't forget to use buses as well as the Tube (tourists often don't venture onto buses, but you see so much more, though it can be slower depending on the route and traffic). You and your son should wear a mask on public transport (unless exempt, though I've been on the tube this morning and people are definitely wearing them less and less since "Freedom Day").
9. You could try a walking tour in the evening. The most well known is London Walk's "Jack the Ripper" walk, not sure if suitable for a 10 year old or not, but there are lots of other walks available.
10. During lockdown we took our kids on one of those self guided treasure hunt type things. We did Locked City's Covent Garden one. It's quite a nice way to explore the area. You get clues of things to look for texted to your phone and walk around trying to find them (plaques, statues etc) and see lots of things you would normally walk straight past.
11. HMS Belfast is good if he has any interest in military history. As is the Cutty Sark (though a bit further away in Greenwich).
12. British Museum is very good (but very big) especially if he has any interest in ancient Egypt. It's the sort of place I wouldn't spend too long with a 10 year old, just focus on a few galleries that you have a particular interest in. They have these "Museum Missions" where you scan the QR code and have to find things or take pictures with certain objects etc.
13. If you are passing through King's Cross there is a HP shop and Platform 9 3/4 photo op (but the photo point gets very busy later in the day). Not sure I would go to King's Cross specifically for this, but if you are passing through and your son likes HP...
That's all I can think of for now! I'm sure I should be able to think of tons more...
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